A geometrical approach to nonlinear perturbations in relativistic cosmology

TL;DR

This paper reviews a covariant, non-perturbative framework for analyzing nonlinear cosmological perturbations, including fluids and scalar fields, facilitating higher-order calculations.

Contribution

It introduces a fully nonlinear, covariant approach to cosmological perturbations applicable to fluids and scalar fields, enabling systematic higher-order analysis.

Findings

Derived a nonlinear extension of the uniform-density curvature perturbation.

Presented evolution equations for nonlinear perturbations in cosmology.

Demonstrated the formalism's capability to handle higher-order perturbations.

Abstract

We give a pedagogical review of a covariant and fully non-perturbative approach to study nonlinear perturbations in cosmology. In the first part, devoted to cosmological fluids, we define a nonlinear extension of the uniform-density curvature perturbation and derive its evolution equation. In the second part, we focus our attention on multiple scalar fields and present a nonlinear description in terms of adiabatic and entropy perturbations. In both cases, we show how the formalism presented here enables one to easily obtain equations up to second, third and higher orders.